Required Reading chapter 17 (See course calendar for optional sections.) Review and Thought Questions p. 401: 6, 7, 10, 13

Introduction

One emphasis of this introductory astronomy course has been how we have learned of the size and age of the Universe, and why we think we are "pretty close" in our understanding of what is actually going on. The distance between the Earth and the Sun forms the baseline for the measured parallax method, the most accurate method, but applicable to only the closest stars. Using our knowledge of the nature of stars and how they evolve, we may have stepped to the use of the spectroscopic parallax method, and learned that although this method is fraught with uncertainties, we can use it to measure the distances to very far away stars. We touched very briefly on the use of comparing the main sequence of two clusters of stars at a given color and determining the relative distances that way. This method, called main-sequence fitting relies on our knowing the accurate distance to the Hyades Cluster in Taurus. Had we more time in the quarter, we may have worked through the lab that finds this distance using the moving cluster method. A still more accurate method of determining distances (and, by the way, becoming a more accurate method with on-going research) can be had with the use of variable stars, such as RR Lyrae and Cepheid variables, so-called "standard candles." Our study of these variables gave us the distances to the globular clusters in the Galaxy and removed our position from the center of the Galaxy to about 2/3 of the way to the edge. These kinds of stars also showed us that the Andromeda galaxy is over 2 million light years away--the Universe is much larger than ever imagined!

But even the luminous Cepheid variables cannot be used for distance determinations much farther than the Virgo supercluster, some 60 million light years away. How do we "know" the distances to galaxies that are estimated to be 8 billion light years away? We must find even more luminous objects--objects for which we think we know the luminosity. White dwarf or Type Ia supernovae may have a maximum luminosity that is a million times greater than that of Cepheids. Observations of these supernovae has given us both estimates of galaxies billions of light years away AND a headache as they seem to reveal a universe whose expansion is accelerating!

We run out of usable standard candles at these objects. From here, we need to rely upon secondary standards: the Tully-Fisher relationship, the "fifth-brightest" elliptical galaxy in a cluster, and most importantly, the Hubble Law.

Learning Objectives After listening to the lecture, reading the text and these on-line notes, and completing the Hubble Law Lab, you should be able to: List the indicators or methods used to determine distances to galaxies in the local group. Define what is meant by a galaxy cluster and a supercluster, and state why these are important for our understanding of the structure of the Universe. List the indicators or methods used to determine distances to galaxies farther away than 5 million light years. State the Hubble Law and explain what is meant by the "Hubble Constant." Explain what information we can get from an accurate measurement of the Hubble Constant. Explain what is meant by "peculiar" motions of galaxies and how these motions affect our measurements of the Hubble Constant. Outline the following methods of determining distances: measured parallax, [spectroscopic parallax,] use of variable stars, cluster main sequence fitting, use of Type 1a (white dwarf) supernovae, and Hubble Law. Optional (depending on the quarter) Give a general description of the kinds of galaxies found in the Local Group and the approximate distances to the major galaxies (accurate to within an order of magnitude).

Terms you should know: Local Group galaxy cluster supercluster standard candle cosmologist cosmological redshift Hubble Constant peculiar motions

Concepts Covered

Galaxy Grouping, Clustering, and Superclustering
Extragalactic Distance Scale
Multiple-Choice Quiz with answers
Relevant Links

Galaxy Grouping, Clustering, and Superclustering

Galaxies seemingly do not like to be alone. Something about the way they were formed a few millions or billions of years after the origin of our universe determined that they would be found in groups, clusters, superclusters, and even larger structures that extend over 100's of millions of light years. We will look first at what our determination of distances has showed us about the structure of the Universe, and then we will review how we know what we do.

The Local Group of Galaxies

Approx. distance: 2.5 million ly	Approx. distance: 3 million ly	Approx. distance: LMC--170,000 ly; SMC--250,000 ly
[Click on each image for an enlarged view.]

Review your text and find out which distance indicator or method would be best to use for galaxies that are within about 5 million light years.

Clusters and Superclusters

[click] Virgo	[click] Coma	[click] Hydra
[click] Hercules	[click] Perseus	[click] Very Distant Cluster

Review your text and find out what standard candles are used for galaxies that are hundreds of light years away. Find out what methods are used for galaxies that are half-way across the Universe. Some of the images have an approximate distance indicated. These distances actually depend on the value of the Hubble constant. Why must their distances depend on the value of the Hubble Constant?

The Extra-Galactic Distance Scale

Questions for a Cosmologist

1. Why are accurate measurements of distances important?

2. What is the Hubble "constant"?

3. Why is an accurate measurement of the expansion rate of the Universe (the Hubble Constant) essential?
4. What is a "cosmological redshift"?

Answers from a Cosmologist

1. To determine the age, size, structure, and fate of the Universe.

   To constrain theories of cosmology and models of galaxy formation.

   To estimate the fundamental quantities:

   • primodial density of hydrogen and helium (deuterium and lithium)
   • the amount of dark matter

2. The Hubble Constant measures the rate of the expansion of the Universe; how the velocities of the galaxies change with the distances away from Earth.

3. An accurate measurement of the Hubble Constant tells us the
   • age of the Universe: Age = 1/H_o (in seconds, with a conversion of units needed to put Mpc into kilometers)
   • size of the Universe: Size = approximately the look-back time
   • fate of the Universe: Fate = ??? (depends on deceleration parameter, or how the Hubble Constant changes with distance)

4. The cosmological redshift is a shifting of the lines of the spectrum of a galaxy due to the wavelengths being stretched by the expansion of space itself. Galaxies are not "flying through space"; they are sitting in space and being carried along by the expansion.

The Hubble Constant

• The Hubble Constant is a measure of the rate of expansion of the Universe. It has units of velocity divided by distance: kilometers per second per megaparsec (km/sec/Mpc).

• Galaxy must be participating in the "Hubble Flow.", meaning that it has to be far enough away that gravity from the Local Group (and to some extent the Virgo Supercluster) has little or no effect on it.

• Hubble constant is difficult to measure because:
  • Galaxies are perturbed by their neighbors thus adding "peculiar" motions
    Peculiar motions refer to the velocities of the galaxies around the center of mass of their respective clusters. The cluster will have some overall measured recessional velocity (we'll call it the average velocity), but those galaxies that are moving towards us will have a slightly lower-than-average velocity and those galaxies that are moving away from us (but still within their cluster) will have a slightly higher-than-average velocity. Thus, at a given distance, there will be a "scattering" of velocities around some average. When you fit the straight line through your data in the Hubble Law Lab, you are essentially fitting the average velocity at each given distance. Peculiar velocities make it harder to determine just where that straight light should go.
  • Obtaining accurate distances has been exceedingly difficult.

• Using the Hubble Law for galaxies far, far away does not result in very accurate distances because we do not know the exact value of the Hubble Constant.

• Once we get the spectrum of a galaxy, determine the redshift of the lines, derive the velocity from the redshift, then: distance = velocity / Hubble Constant.

• Accurate measurements of radial velocities are very important.

  One can see from this relationship that if the Hubble constant is a small number, the distance is large. If the Hubble constant is a large number, then the distance is small (astronomically speaking!). For example, let's say we measure the velocity of a galaxy to be 60,000 km/sec. If we assume a Hubble constant of 60 km/sec/Mpc, then we calculate a distance of 1,000 Mpc. If we, on the other hand, assume a Hubble constant of 80 km/sec/Mpc, then the galaxy is 750 Mpc away. Now, the galaxy is NOT at 2 different distances! It is just our inability to zero-in on an accurate value for the Hubble constant that limits our knowledge of distances using the Hubble Law.